Answer
The function is discontinuous at every $ x=n $. The discontinuity here is a jump discontinuity. Moreover, the function is left continuous.
Work Step by Step
We know that the function $[x]$ has a jump discontinuity and is left continuous at $ x=n $. Thus, the function
$$\cos \pi[x]$$
is discontinuous at every $ x=n $. The discontinuity here is a jump discontinuity. Moreover, the function is left continuous.
